Chrome alum can be used to harden both raw emulsions before coating and as a hardener during processing. This solution is quite toxic. Handle with care.
For coating, I make a 10% solution in water and add about 5 ml / 200 ml of 10% gelatin. The hardness is about the same over that range, but the length of time needed to achieve good hardness varies from 24 hours to about 96 hours.
Yes, the Chrome Alum and Alum hardeners act by forming an ionic bond with gelatin. The Aluminum based Alum can be reversed and the film or paper can become softer, but I am not sure about Chrome Alum due to its strength. In addition, Chrome Alum forms a bond with glass plates.
Formaldehyde forms a covalent bond with gelatin and once formed it is very difficult to reverse! So the bonds are totally different in nature and in effect. As you go from formalin to glyoxal to succinaldehyde to glutaraldehyde, you also form a "longer" bond length which changes the characteristic of the hardening.